If anything on a horse's head is cutting off air supply, then it is adjusted 9 miles of wrong.
Like Chick said, using a bosal effectively is an art form and it does take a long time to learn how to keep a horse from calling your bluff in one of them. Most folks who ride around in bosals or halters are all happy because their horse will stop/turn a little bit while plodding around but if you ever actually asked them to do something with the horse, they would have zero control
A (real)hackamore, or halter with both reins attached under the chin does have a different feel, so for a horse that's trained with only direct rein pressure, or one that's learned to evade, or just not learned to yield effectively to other cues, some 'back to basics' lessons are important, then a few rides at least in a safe environment prudent before going out & about in it.
But as for it being such an 'art form' way different to teaching a horse to yield to a bit, and going on about 'calling bluff', that's just wrong IME. Perhaps it may be seen as such for people who rely on pain to force a horse to do stuff, but if they don't use a bit in that way, there's no huge difference(tho you can hurt a horse with a halter, bosal & particularly with a mechanical bitless contraption too). Even if you do like to control with strong force, horses 'call bluff' and refuse to yield to bit pressure too, just think about all the 'harsher bit' & 'my horse won't stop' threads. It's down to good or bad riding/training IMO, not the 'tool'.
As a matter of fact, I find 'spoiled' horses who have learned to evade or otherwise react to bit pressure *generally*(not always) go better in a halter. When 'retraining', I also start in a halter & find problems often just seem to melt away without much effort. Suppose it's my 'safety chain' but for confirmed 'bolters' or such that I'm training, usually the first rides out I do with both halter and bitted bridle, for Justin, but I find it's extremely rare that I feel the need to resort to the bit reins for extra control.